Well, you CAN precompose the particle layer, increase the resolution of the precomp and contents, then just scale up the layer in the master comp. But that'll make everything about the effect bigger, not just the lines.
Put "CC Particle World tutorial" into any search engine. You will find many useless youtube clips and a couple of helpful and superbly done tutorials, too. The thing about Particle World is that it's far more difficult to use than you think because the effect actually lives in a 3D space but only interacts with 2D layers (until you get into some truly advanced functions like programming the emitter's position keyframes in z space and using the Floor functions to simulate the presence of a 3D layer in the main comp).